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BE_110_HW_6 - BE 110 Homework Assignment#6 An Introduction...

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BE 110 An Introduction to Biomechanics Fall 2005 Homework Assignment #6 Due Tuesday 11/15/05, 8AM before class 1. Reading assignment Study the geometric interpretation of the infinitesimal strains, e.g. the strains without the non- linear form of the displacement gradients. See Section 5.4. 2. Practice Problems (a) A small square piece of skin with edge length 1 cm x 1 cm with constant thickness of 1 mm is stretched in its plane by 10% in x–direction, 2 % in y-direction. The tissue is incompressible. Assume the deformation is homogenous (i.e. the displacement is a linear function of x, y, z). What are the displacements in the tissue if its left lower corner remains at the origin. What are the Lagrangian strains? (b) A square plate is sheared by 30 o into a parallelogram as shown in Figure P5.9. What are the strain components. (For solution see Problem 5.9). (c) Derive an expression for the change of (infinitesimal) volume per unit tissue volume using the infinitesimal strain components ε ij .
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